Analyzing the Setup
The problem presents us with an unknown organic compound A having the molecular formula C4H8
The first thing we should always do when given a molecular formula is to calculate its Degree of Unsaturation (DU).
The formula for DU is:
DU=C+1−2H+2N−2X
Plugging in our values:
DU=4+1−28=1
A degree of unsaturation of 1 implies that compound A could either be an alkene (containing one double bond) or a cycloalkane (containing one ring). However, the problem states that compound A undergoes ozonolysis and reacts with acidic KMnO4. These are classic reactions of carbon-carbon double bonds, confirming that compound A is indeed an alkene.
The Ozonolysis Clue
Compound A undergoes ozonolysis to yield compound B, which has the formula C3H6O.
Ozonolysis is a cleavage reaction that breaks the C=C double bond, replacing it with two C=O bonds. Since our starting alkene A has 4 carbon atoms and one of the products (B) has 3 carbon atoms, the other product must contain exactly 1 carbon atom. The only possible 1-carbon product from ozonolysis is formaldehyde (HCHO).
Now, what is compound B? With the formula C3H6O and a DU of 1, it must be a carbonyl compound. The two possibilities are:
1. Propanal (CH3CH2CHO) - an aldehyde.
2. Acetone (CH3COCH3) - a ketone.
The Master Equation
Acidic KMnO4
To distinguish between propanal and acetone, we look at the second reaction. Compound A reacts with acidic KMnO4 to yield the exact same compound B.
Acidic KMnO4 is a powerful oxidizing agent. It cleaves the double bond similarly to ozonolysis but with a crucial difference: it further oxidizes any resulting aldehydes into carboxylic acids. Ketones, on the other hand, are resistant to further oxidation under these conditions and remain intact.
If compound B were propanal, the acidic KMnO4 would have oxidized it into propanoic acid (CH3CH2COOH). Since compound B survives the strong oxidation, it must be a ketone. Therefore, compound B is acetone (CH3COCH3).
(Note: The 1-carbon fragment, formaldehyde, is oxidized completely to CO2 and H2O by KMnO4.)
Final Calculation
Reconstructing Compound A
Now that we know the products of the cleavage are acetone and formaldehyde, we can easily reconstruct the original alkene A.
The trick is to place the oxygen atoms of the two carbonyl products face-to-face, remove them, and stitch the carbon atoms back together with a double bond:
(CH3)2C=O+O=CH2→(CH3)2C=CH2
The resulting structure is 2-methylpropene (also known as isobutylene). This perfectly matches the molecular formula C4H8 and satisfies all the chemical reactions described in the problem.